Venn Diagrams

This picture is an example of a 4-set Venn diagram.

I notice four main rectangles: red, blue, yellow, and grey.I notice that each region contains a unique combination of colors.I wonder how many regions there are.I wonder if there is a region that contains all four colors.I wonder if the diagram includes all possible combinations of the four colors.I notice that the diagram has symmetry.

I notice that this Venn diagram is made of rectangles rather than circles.I wonder if there are other ways to create a 4-set Venn diagram.I wonder if I could make a 4-set Venn Diagram using only circles.I wonder how many regions a 5-set Venn diagram would need to have.I wonder if it is possible to make a 5-set Venn diagram.I wonder if a 5-set Venn diagram can have symmetry.I wonder what is the best way to keep track of the regions so that I don't miss any.I wonder if there is a pattern to the number of regions that an n-set Venn diagram would need to have.I wonder if it is possible to make all n-set Venn diagrams (where n can be any counting number).

For an introduction to Venn Diagrams in general, look here at Purplemath. For a brief look at 4-set Venn diagrams, look here. For more detail, try the Mathematics Stack Exchange, a question and answer site for math at all levels!